Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer

Integrated photonic devices are poised to play a key role in a wide variety of applications, ranging from optical interconnects1 and sensors2 to quantum computing3. However, only a small library of semi-analytically designed devices is currently known4. Here, we demonstrate the use of an inverse design method that explores the full design space of fabricable devices and allows us to design devices with previously unattainable functionality, higher performance and robustness, and smaller footprints than conventional devices5. We have designed a silicon wavelength demultiplexer that splits 1,300 nm and 1,550 nm light from an input waveguide into two output waveguides, and fabricated and characterized several devices. The devices display low insertion loss (∼2 dB), low crosstalk (<−11 dB) and wide bandwidths (>100 nm). The device footprint is 2.8 × 2.8 μm, making this the smallest dielectric wavelength splitter. Electronic hardware description languages such as Verilog and VHDL are widely used in industry to design digital and analogue circuits6,7. The automation of large-scale circuit design has enabled the development of modern integrated circuits that can contain billions of transistors. Photonic devices, however, are effectively designed by hand. The designer selects an overall structure based on analytic theory and intuition, and then finetunes the structure using brute-force parameter sweep simulations. Due to the undirected nature of this process, only a few degrees of freedom (two to six) are available to the designer. The field of integrated photonics would be revolutionized if the design of optical devices could be automated to the same extent as circuit design. We have previously developed an algorithm that can automatically design arbitrary linear optical devices5. Our method allows the user to ‘design by specification’, whereby the user simply specifies the desired functionality of the device, and the algorithm finds a structure that meets these requirements. In particular, our algorithm searches the full design space of fabricable devices with arbitrary topologies. These complex, aperiodic structures can provide previously unattainable functionality, or higher performance and smaller footprints than traditional devices, due to the greatly expanded design space5,8–14. Our algorithm uses local-optimization techniques based on convex optimization15 to efficiently search this enormous parameter space. Here, we demonstrate the capabilities of our inverse design algorithm by designing and experimentally demonstrating a compact wavelength demultiplexer on a silicon-on-insulator (SOI) platform. One of the key functions of silicon photonics is wavelength division multiplexing (WDM), which multiplies the data capacity of a single optical waveguide or fibre-optic cable by the number of wavelength channels used16–18. Unfortunately, conventional wavelength demultiplexers such as arrayed waveguide gratings19, echelle grating demultiplexers20 and ring resonator arrays21 are fairly large, with dimensions ranging from tens to hundreds of micrometres22. Our device has a footprint of only 2.8 × 2.8 μm, which is considerably smaller than any previously demonstrated dielectric wavelength splitter23. Let us now consider the general formulation of the inverse design problem for optical devices. We choose to specify the performance of our device by defining the mode conversion efficiency between sets of input modes and output modes at several discrete frequencies. These modes and frequencies are specified by the user and kept fixed during the optimization process. In the limit of a continuous spectrum of frequencies, any linear optical device can be described by the coupling between sets of input and output modes, making this a remarkably general formulation24. Suppose the input modes i = 1...M are at frequencies ωi and can be represented by equivalent current density distributions Ji. The electric fields Ei generated by the input modes should then satisfy Maxwell’s equations in the frequency domain,